The cosmic microwave background (CMB) temperature maps from the Wilkinson
Microwave Anisotropy Probe (WMAP) are of great importance for cosmology. After
finding out significant systematics in official WMAP maps, we had developed our
own map-making software independently of the WMAP team. The new maps produced
from the WMAP raw data and our software are notably different to the official
ones, and the power spectrum as well as the best-fit cosmological parameters
are significantly different too. By revealing the inconsistency between the
WMAP raw data and their official map, we pointed out that there must exist an
unexpected problem in the WMAP map-making routine. Here we state that the
trouble comes from the inaccuracy of antenna pointing direction caused by
improper offset of the quaternion interpolation in the WMAP routine. The CMB
quadrupole in the WMAP release can be generated from a differential dipole
field which is completely determined by the spacecraft velocity and the antenna
directions without using any CMB signal. After correcting the WMAP team's
error, the CMB quadrupole component disappears. Therefore, the released WMAP
CMB quadrupole is almost completely artificial and the real quadrupole of the
CMB anisotropy should be near zero. Our finding is important for understanding
the early universe.

Gary Hinshaw gave a nice talk at the Moriond conference where he addressed the issue raised in this paper. My understanding is that WMAP take the pointing to be the mid-point of the scan during each sampling period (a distance of ~7arcmin), but Liu & Li take it at the start. The WMAP team can reproduce the result of this paper by using the alternative pointing, though clearly it makes much less sense (i.e. WMAP is correct).

There is a response from Prof. Hinshaw through e-mail and we have
given a reply. I think I could not give more details of the discussion without
his permission, but I can give a crucial point: We have found that the
WMAP spacecraft attitude and the differential data are not recorded
synchronously. The attitude data are recorded 25.6 ms later than the
differential data. Therefore it's self-evident that we must extrapolate the
quaternion to earlier times to match the differential data. This is right
consistent to our setting that uses earlier quaternion than WMAP. However,
our previous offset setting is equivalent to 51.2 ms rewind in Q-band and
25.6 ms rewind in W-band; therefore, we need more work to confirm
which is better (25.6 or 51.2).

Maybe for most readers, it's much better to see the same problem in a
more simple way: if the quaternion is recorded right at the center of the
observation, then all we have to do is to use it directly and there is no
need to computer the "center" again. This is exactly the case for W-band.

It's very easy to check the time drift between WMAP quaternion and
differential data without mapmaking, just use the fv tool (http://
heasarc.gsfc.nasa.gov/docs/software/ftools/fv/) to open ANY fits format
WMAP TOD file, and check the first time record in the Meta Data Table
(contains the quaternion) and the Science Data Table (contains the
differential data). There is an almost constant difference between them
that is about 2.963E−7 in reduced Julian time (25.6 ms), with the
quaternion time being later than the differential datum time.

More details can be found in the update of this article (V2) on arxiv.

This is very interesting if true. The authors focus on a spurious quadrupole generated by the combination of pointing (interpolation) errors and the large dipole (due to motion wrt to the CMB).

If this pointing-error idea of Liu and Li is correct, then presumably the WMAP dipole is also slightly incorrect. Its not clear how much it would change because of the complicated scan pattern of WMAP (i.e. I guess its not a simple rotation of the dipole) .... but the order of magnitude might be around the 10 microK as mentioned earlier in this thread.

This is about the same magnitude as the dipole-behind-clusters signal claimed earlier by Kashlinsky et al.
http://cosmocoffee.info/viewtopic.php?t=1227 (and there is also a more recent paper 0910.4958) who interpreted as being a kinetic SZ effect. Recall that they took the dipole-subtracted WMAP map, filtered it further on large scales to reduce the intrinsic CMB fluctuations, and then calculated the dipole of temperatures at the locations of rich clusters. From this dipole they infer a large-scale bulk flow of clusters.

It would be interesting to repeat their measurement on the Liu and Li maps.

Here are some data that may help the readers to understand the time
drift issue:

There are 1875 records in one day's TOD, 30 frames in each record, and
30 observations in each frame (W-band), i.e., 1875*30*30=1,687,500
observations in 24 hours. Thus each observation lasts for
24*3600*1000/1,687,500=51.2 ms

The quaternion is recorded 25.6 ms after the start of each frame, i.e.,
right at the center of the observations.

A priori, if we ignore the last few comments above, there is a
reasonable chance that Liu and Li could have made a human error and
accidentally made an assumption in their analysis method that
happened to anti-correlate with the cosmological component of the
quadrupole, mostly cancelling it out. It is clear from 0907.2731
that in July 2009, they were not aware of what they did differently
from the WMAP team regarding the spacecraft attitude.

However, in that case, it would be reasonable that the strongest
anti-correlation would be for an offset a little further away. So, by
considering the timing offset to be a free parameter, it should be
possible to find an optimal offset that anti-correlates with the
cosmological quadruole even more strongly. The argument should then
shift to more first principle methods - which offset should in principle
be correct (e.g. as in the last few comments)?

But have a look at Table 1 and Figure 3 of v2 of the paper! The following
graph shows the 10 values explicit in Table 1 and the 1 value implicit
in it, assuming that I have understood correctly.

As stated in the paper, the two halves of the plot appear to be very
linear, with slope 14.6±0.2μK / full_offset, and the minimum
appears to occur very sharply at the point that Liu and Li used. It
seems to be stretching the limits of credibility that Liu and Li
happened by chance to find a very sharp optimal point for
anti-correlating the cosmic quadrupole signal.

Is it reasonable that this is so linear? Wouldn't we expect some more
complicated mix of e.g. trigonometric functions etc? The obvious answer
is that getting a Taylor expansion that is linear to first order happens
in many situations. A plot of | sin(δ) | , where − 7' < δ < 7',
gives a plot identical to the above, apart from scaling.

A formal statistical exercise would be to calculate more and more
offsets closer and closer to the minimum, until the level where noise
(and doing things correctly like sidereal day vs WMAP-day vs
Earth-day) make it difficult to get a preciser estimate of the minimal
offset. At the moment, if we ignore our intuition that the minimum is
very sharp, we could presumably say that if Liu and Li chose an
arbitrary offset in their initial (July 2009) analysis, then they had
a 10% chance of finding this minimum (that they were not looking for).
That's not (yet) a strong rejection. Ten more calculations with
, where δ is the
timing offset fraction as before, should get to a 99% rejection of
Liu & Li finding the minimum by chance.

Another extension would be to go around and beyond ±0.5, e.g.
δ = 0.45, 0.48, 0.5, 0.52, 0.55, 0.6, 0.7, 0.8, 0.9, 1.0, 2.0,
3.0 to see if at least some sort of feature occurs at the value of
the WMAP team's offset (the sign convention is + 0.5 in Fig. 3).
If this function turns out to be linear with no sign of
anything at all except at δ = 0, then I suspect that the "Axis
of Evil" problem will be replaced by the WMAP Evil Attitude
effect: WMAP's spacecraft attitude evilly hid itself from the WMAP
team and from many other cosmologists for seven years...

The attitude data are recorded 25.6 ms later than the
differential data. ... It's very easy to check the time drift between WMAP quaternion and
differential data without mapmaking, just use the fv tool (http://
heasarc.gsfc.nasa.gov/docs/software/ftools/fv/) to open ANY fits format
WMAP TOD file, and check the first time record in the Meta Data Table
(contains the quaternion) and the Science Data Table (contains the
differential data). There is an almost constant difference between them
that is about 2.963E−7 in reduced Julian time (25.6 ms), with the
quaternion time being later than the differential datum time.

You're right. fv version 3.0−17 gave me a segmentation violation, but gui's are not needed here anyway. This can be checked using GDL and the IDL astro library FITS tools as follows.

; print some examples
print,'quaternion time minus data time in s: first 10 frames of the day'
print,offset[0:9],format="(d15.7)"
print,'quaternion time minus data time in s: last 10 frames of the day'
print,offset[1865:1874],format="(d15.7)"

Quote:

The attitude data are recorded 25.6 ms later than the differential data.

For a few TOD files that I randomly selected, I get 25.6000 ms offset, which is enough to make your statement very credible.

For a more fundamental check (rather than doing this for all data files), WMAP engineers should in principle be able to check the code that generates the timestamps in the "Science Data Table" and explain how this relates to the spacecraft attitude quaternions in the "Meta Data Table". They should be able to find the half-individual-observation-offset in that code. The alternative is that WMAP people point us to the specific section in one of the WMAP technical papers where the quaternion versus science frame 25.6 ms offset has already been explained. I searched and failed to find it.

The WMAP team has updated their Explanatory Supplement paper just a few hours ago (20100405094148−04'00'): http://lambda.gsfc.nasa.gov/product/map/dr4/pub_papers/sevenyear/supplement/WMAP_supplement.pdf
On page 117 (125th page in file) in the Meta Data Table section, "Attitude data are transmitted from the spacecraft every second. The thirty quaternions corresponding to the science data frames have been interpolated to the start time of the corresponding science frame." Here, "interpolated" presumably means interpolation between successive seconds when attitude data are sent from the spacecraft to Earth. This is not the issue we're interested in here.

A few sentences later, "The rapidly-varying quaternions have been specifically interpolated to the start time of each 1.536 sec science frame." This is the interpolation we're interested in. This says "start time", without mentioning the 25.6 ms offset.

On the following page, in the Science Data Table section, again nothing is stated about the 25.6 ms offset.

; print some examples
print,'quaternion time minus data time in s: first 10 frames of the day'
print,offset[0:9],format="(d15.7)"
print,'quaternion time minus data time in s: last 10 frames of the day'
print,offset[1865:1874],format="(d15.7)"

A clarification: that should read "first 10 major science frames" and "last 10 major science frames".

Sorry for chiming in late, but unless I misunderstand the situation completely, there are a couple of very simple tests that could rule out this effect. If your pointing data and your detector data are offset in time, then where a source ends up in your sky map depends on the direction of the scan(s) used to make that sky map. If you made a map from only "left"-scanning data and another map from only "right"-scanning data, sources would show up in different places in the two maps. The offset between the two maps in the case of Liu et al.'s model would be 14 arcminutes. If you ignored the offset and added the two maps together, you'd get two copies of every source — or, if your beams were on the same scale as the offset, you'd get very smeared-out sources.

So, there are two families of tests that can easily check for this effect:

1) Beam tests. Is there evidence of many-arcminute-scale smearing of WMAP beams? I think the answer to this is a resounding "no". The WMAP beams are estimated from in-flight measurements of Jupiter, and they use the same pointing data as the CMB measurements do, so they should suffer the same offsets. There is no way a 7' or 14' beam smearing would have gone undetected, particularly in W band, where the beam scale is only 12'. (Page et al. (2003) say right in the abstract that the WMAP beams "closely follow the prelaunch expectations.") If the WMAP team somehow managed to analyze the Jupiter data differently from the CMB data, such that the Jupiter beams are correct, then we'd see a discrepancy between the assumed beams and the real (smeared) beams in the CMB data, and the high-ell WMAP CMB power spectrum would not agree so well with the small-scale experiments (ACBAR, QUaD, SPT, ACT). (Thanks to Akito Kusaka for pointing that out.)

2) Source offset tests — i.e., do the test described above of making sky maps with data in only one scan direction at a time, and compare the maps. Even easier: Find some WMAP TOD where Jupiter was observed from one scan direction (say, increasing R.A. and constant dec) and some other WMAP TOD where Jupiter was observed from the opposite scan angle (in this case, decreasing R.A. and constant dec). Plot the detector timestreams vs. sky coordinate (in this case R.A.). If the offset claimed by Liu et al. is there, you should see two Jupiters, separated by 14'.

As stated in the paper, the two halves of the plot appear to be very
linear, with slope 14.6±0.2μK / full_offset, and the minimum
appears to occur very sharply at the point that Liu and Li used. It
seems to be stretching the limits of credibility that Liu and Li
happened by chance to find a very sharp optimal point for
anti-correlating the cosmic quadrupole signal.

Liu & Li seem to have subtracted off the map at the offset they hypothesise to be correct, rather than subtract off the rms at that offset. So the sharp minimum here does not mean what I thought it did. The question of where the minimum quadrupole lies and whether or not this occurs close to the offset (or one of the two offsets, −25.6 and −51.2 ms relative to the official WMAP offset) proposed by LL remains an open question.

Sorry for chiming in late, but unless I misunderstand the situation completely, there are a couple of very simple tests that could rule out this effect.

Tom: nice idea! The effect is not as obvious as you guessed, but after
a bit of work, it does show that an error did not occur in putting
together the calibrated TOD into maps: 1004.4506. A timing error
at this step is rejected at high significance.

What remains possible is that the time offset occurred during the calibration
step - which uses the dipole. Of course, this would require that while the
people who put together the calibrated TOD correctly ignored the stated time
offset, the people who did the calibration incorrectly assumed that the stated
time offset or a closely related offset was correct. It also reqiures that the
people who did the calibration either didn't notice that the 25.6 ms offset
was not mentioned in the Explanatory Supplement, or noticed and forgot
for the past 7 years to ask someone to update it. Or the software read
in the time from the meta data and nobody noticed it was offset from the science
data times. IMHO it's still credible that an error occurred and nobody noticed
(until Liu et al. 1003.1073...).

Any neat ideas on how to test a timing offset error during the
calibration? There's probably no clean way to do this without preparing
a pipeline for converting uncalibrated TOD to calibrated TOD, and even
after doing that correctly, it's not obvious to me that it would
be easy to reject either hypothesis (no timing error, or timing error
of −25.6 or −51.2 or −76.8 ms).

BTW, here's a schematic diagram of the timing offset in the calibrated, filtered 3-year TOD files that I checked. It's also
present in a few uncalibrated 3yr TOD files that I checked.